Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
def give_tri(a2):
    return a2*(a2+1)/2
def check_tri(a3):
    p=int((2*a3)**0.5)
    if a3==0:
        return False
    elif p*(p+1)==2*a3:
        return True
    else:
        return False
def check_cool(a1):
    j=int(a1**0.5)
    while j>=1:
        k1=a1-give_tri(j)
        if check_tri(k1):
            return True
        else:
            j=j-1
n=int(input())
if check_cool(n):
    print("YES")
else:
    print("NO")